Hey!

When we consider a polynomial, say cubic, we say that its graph will cut the x axis at atmost 3 points and the x co-ordinates of those points will the roots of the polynomial.

But sometimes the graph of a cubic polynomial may cut the x axis at a single point, for example the graph of y = x^3 and this means that THIS POLYNOMIAL HAS 3 IDENTICAL ZEROES each equal to 0 {bcoz y = (x-0)(x-0)(x-0)}

But is it the case every time? Well, if the graph of a cubic polynomial cuts the x axis at one point, can it NOT mean that

1) the other two of its roots are complex and not real values (btw, that is true if we consider this: y = x^3 - 1)

2) my real question is, can it happen that the other two roots do not exist at all? Not even in the complex world? So that we can say "the other two roots do not exist and hence it cuts the x axis once only......"

So, cutting of the x axis just once by a cubic polynomial means basically what, if someone asks us what should we tell - is it 3 equal roots? Or 1 real and rest complex roots.....all these things we cannot discern from the graph alone and we need to look at the equation, right?? Such a graph means just that there will be one real root and not sure about the status of others i.e.being equal to it or being complex?